Magnetothermodynamics of α-NiSO4·6H2O. IV. Heat Capacity, Entropy, Magnetic Moment, and Internal Energy from 0.4° to 4.2°K with Fields 0–90 kG along the a Axis

Abstract

The heat capacity and magnetic moment of a 4‐cm‐diam spherical single crystal of α‐NiSO₄·6H₂O have been measured over the range 0.4°–4.2°K, with stabilized magnetic fields of 0, 5, 10, 15, 25, 40, 65, and 90 kG along the $a$ crystallographic axis. Comparison with our previous data with the field along the bisector of the $\mathrm{a,\; b}$ axes confirms the observation of Bose and Schoenberg that the magnetic characteristics in the $\mathrm{a,\; b}$ plane of this tetragonal crystal are not isotropic. The heat capacity and entropy of the lattice and electronic system approach zero at the lower temperatures and all fields. These data and closely interlocked observations of temperature vs magnetic field on isentropes which crossed the heat‐capacity curves enabled an accurate tabulation of the entropy as a function of field and temperature. The derived differential magnetic susceptibility, the internal energy, enthalpy, and magnetic work are tabulated. At 90 kG the proton spins were in good equilibrium with the lattice above 1.1°K and were essentially out of equilibrium below 0.9°K. Details of heat‐capacity measurements, out of equilibrium, in partial equilibrium, and in rapid equilibrium with the nuclear spin system are presented. With minor deviations it was found possible to represent the heat‐capacity observations at all fields by means of three‐state Schottky functions. The separations of the three states combined with the change of enthalpy of the ground state $W_0$ with field enabled evaluation of the Zeeman pattern for the $W_0{\mathrm{,\; W}}_1$ , and $W_2$ states between 0 and 90 kG. The $W_1$ and $W_2$ states were found to be degenerate in zero field. All of the observations were found to be in excellent agreement with values calculated from the spin‐Hamiltonian–molecular‐field parameters derived by Fisher and Hornung from previous observations with the field along the $c$ axis together with those obtained when the field was along the bisector of the $\mathrm{a,\; b}$ axes.